On first-order μ-calculus over situation calculus action theories
De Giacomo G
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In this paper we study verification of situation calculus action theories against first-order mu-calculus with quantification across situations. Specifically, we consider muLa and muLp, the two variants of mu-calculus introduced in the literature for verification of data-aware processes. The former requires that quantification ranges over objects in the current active domain, while the latter additionally requires that objects assigned to variables persist across situations. Each of these two logics has a distinct corresponding notion of bisimulation. In spite of the differences we show that the two notions of bisimulation collapse for dynamic systems that are generic, which include all those systems specified through a situation calculus action theory. Then, by exploiting this result, we show that for bounded situation calculus action theories, muLa and muLp have exactly the same expressive power. Finally, we prove decidability of verification of muLa properties over bounded action theories, using finite faithful abstractions. Differently from the muLp case, these abstractions must depend on the number of quantified variables in the muLa formula.
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